Lattice calculation of $1/p^2$ corrections to $\hat{I}{\pm }_s$ and of $\hat{I}{›}_{\mathrm{QCD}}$ in the $\widetilde{MOM}$ scheme

Abstract

We report on very strong evidence of the occurrence of power terms in $\as(p)$, the QCD running coupling constant in the $\widetilde{MOM}$ scheme, by analyzing non-perturbative measurements from the lattice three-gluon vertex between 2.0 and 10.0 GeV at zero flavor. While putting forward the caveat that this definition of the coupling is a gauge dependent one, the general relevance of such an occurrence is discussed. We fit $\hat{I}{›}_{\overline{\mathrm{MS}}}^{(n_f=0)}=237\pm 3_{-10}^{+0}$ MeV in perfect agreement with the result obtained by the ALPHA group with a totally different method. The power correction to $\as(p)$ is fitted to $(0.63\pm 0.03_{-0.13}^{+0.0}){\mathrm{GeV}}^2/p^2$.

21 pages, 3 figures